Derivative superconvergent points in finite element solutions of poisson's equation for the serendipity and intermediate families - A theoretical justification

Mathematics of Computation

Volumn 67, Issue 222, 1998, Pages 541-552

  Zhang, Zhimin ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032360610     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-98-00942-9     Document Type: Article

References (7)

1. I. Babuška, T. Strouboulis, C.S. Upadhyay, and S.K. Gangaraj, Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations, Numerical Methods for Partial Differential Equations 12 (1996) 347-392. MR 97c:65160
2. C.-M. Chen, Superconvergent points of Galerkin's method for two-point boundary value problems (in Chinese), Numer. Math. J. Chinese Univ. 1 (1979), 73-79.
3. J. Douglas, Jr., T. Dupont, and M.F. Wheeler, An L∞ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials, RAIRO 8 (1974), 61-66. MR 50:11812
4. N.N. Lebedev, Special Functions and Their Applications, Dover, New York, 1972. MR 50:2568
5. A.H. Schatz, I.H. Sloan, and L.B. Wahlbin, Superconvergence in finite element methods and meshes which are symmetric with respect to a point, SIAM Journal on Numerical Analysis 33(2) (1996), 505-521. CMP 96:12
6. B. Szabó and I. Babuška, Finite Element Analysis, John Wiley & Sons, New York, 1991. MR 93f:73001
7. L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605, Springer, Berlin, 1995. CMP 97:09